Work and energy: a first look

Lifting a 2 kg bag onto a 1.5 m shelf takes about 29 joules of work, and the bag gives the same 29 J back if it falls.

Work: force times distance

In physics, work has a precise meaning. When a force moves something, the work done is the force times the distance moved in the direction of the force: W = F d. Work is measured in joules (J), and 1 J = 1 N × 1 m. Push a trolley with 100 N for 3 m and you do 300 J of work. Lift a 2 kg bag at steady speed onto a 1.5 m shelf and you push up with a force equal to its weight, 2 × 9.81 = 19.6 N, over 1.5 m, so the work is about 29 J.

The direction matters. If you carry the same bag across a level room, your arms push up while the bag moves sideways, so in the physics sense the upward force does no work on it, even though your arms get tired. And if you push against a wall that does not move, the distance is zero, so the work is zero.

Energy: the ability to do work

Energy is what lets something do work, and it is also measured in joules. Two kinds appear in every motion problem. Kinetic energy is the energy of movement: KE = ½ m v². A 1,000 kg car at 20 m/s has ½ × 1,000 × 20² = 200,000 J. Because of the v², doubling the speed gives four times the kinetic energy, which is why stopping distances grow so fast with speed. Gravitational potential energy is energy stored by height: PE = m g h. The 2 kg bag on the 1.5 m shelf has about 29 J more than it did on the floor, exactly the work you did lifting it.

Energy changes form but the total stays

Drop a ball from a height h. As it falls it loses potential energy and gains kinetic energy, and without air the two always add up to the same total. Setting m g h = ½ m v² gives the speed at the bottom, v = √(2 g h). From 5 m that is about 9.9 m/s; from 20 m, about 19.8 m/s, the same answers that the free-fall equations give. The mass cancels again, just as it did in Newton’s second law.

The pendulum in the lab shows the same exchange over and over. At the ends of the swing the bob is highest and stopped: all potential energy. At the bottom it is lowest and fastest: all kinetic. A 1 m pendulum released at 60° drops 0.5 m and passes the bottom at √(2 × 9.81 × 0.5) ≈ 3.1 m/s. In a real pendulum a little energy goes into the air and the pivot as heat on every swing, so it slowly dies down. Friction does not destroy energy; it turns it into heat, which is harder to use. The Energy course goes further into these ideas.

How fast work is done is called power: P = W ÷ t, measured in watts (W), where 1 W = 1 J per second. A 60 kg person climbing 3 m of stairs does 60 × 9.81 × 3 ≈ 1,766 J of work against gravity. Doing it in 5 s takes about 353 W; strolling up in 15 s takes about 118 W. The work is the same either way, which is why running upstairs leaves you out of breath while walking up does not: the energy is the same, but you deliver it three times faster.